The nature talisman is used to gain access to the nature altar, located north of Shilo Village on the island of Karamja, where players can craft nature runes. The talisman can also be combined with a tiara at the nature altar by having both the nature talisman and tiara in your inventory, and using the tiara on the altar. This action grants the player 45 Runecraft experience; many players choose to do this in order to save an extra inventory space and make quicker trips when crafting nature runes, as the nature altar may be accessed simply by left-clicking on it while the player is wearing the nature tiara.
A good way to obtain the talisman is to kill abyssal leeches in the abyss after completing the Enter the Abyss miniquest. Keep in mind that the abyss is very dangerous and you may find yourself quickly overwhelmed without proper armour and food. Always bring a teleport in case you need a quick escape. The nature talisman is also a part of the rare drop table, therefore any monster with access to the rare drop table has a chance of either dropping this talisman or a chaos talisman (with a couple of exceptions being able to drop both, such as fire giants and abyssal demons).
For an exhaustive list of all known sources for this item, see here